Institute of Mathematics AS CR, v. v. i.
Not a member yet
44818 research outputs found
Sort by
Continuous adjoint approach to shape optimization with respect to 2D incompressible fluid flow
No full textsummary:The aim of this article is to briefly introduce the procedure for optimizing water turbine blades, which can lead to an innovative blade design and, consequently, an improvement in the desired properties of the water turbine, such as efficiency or the preferred pressure distribution on the blade. The computational method is based on formulating an objective function under certain constraint conditions, which are governed by the Navier-Stokes equations. This formulation enables the use of the Lagrange multiplier method, which incorporates the constraints into the augmented objective function. We derive the so-called adjoint problem, allowing us to simplify the gradient formulation for the chosen gradient-based optimization method
On fluid structure interaction problems of the heated cylinder approximated by the finite element method
No full textsummary:This study addresses the problem of the flow around circular cylinders with mixed convection. The focus is on suppressing the vortex-induced vibration (VIV) of the cylinder through heating. The problem is mathematically described using the arbitrary Lagrangian-Eulerian (ALE) method and Boussinesq approximation for simulating fluid flow and heat transfer. The fluid flow is modeled via incompressible Navier-Stokes equations in the ALE formulation with source term, which represent the density variation due to the change of temperature. The temperature is driven by the additional governing transport equation. The equations are numerically discretized by the finite element method (FEM), where for the velocity-pressure couple the Taylor-Hood (TH) finite element is used and the temperature is approximated by the quadratic elements. The proposed solver is tested on benchmark problems
Některá využití harmonického průměru ve výuce matematiky na střední škole
Get PDFsummary:Článek představuje základní poznatky o harmonickém průměru a demonstruje jeho možná využití při řešení středoškolských úloh z matematiky. V navazujícím příspěvku se zaměříme na využití harmonického průměru ve fyzice a finančnictví
Jak změřit difuzní koeficient pomocí laseru?
Get PDFsummary:Článek popisuje sestavení jednoduchého experimentu pro měření difuzního koeficientu. Při analýze tohoto pokusu je třeba spojit znalosti z informatiky, matematiky i fyziky. Vzhledem k tomu, že difuzi se na středních školách věnuje většinou relativně málo prostoru a žáci tomuto tématu často dostatečně neporozumí, je popisovaný pokus vhodný k doplnění těchto znalostí
Finite-time observability of probabilistic Boolean multiplex control networks
Get PDFsummary:This paper investigates the finite-time observability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, the finite-time observability of the PBMCNs is converted into the set reachability issue according to the parallel interconnection technique (a minor modification of the weighted pair graph method in the literature). Secondly, the necessary and sufficient condition for the finite-time observability of PBMCNs is presented based on the set reachability. Finally, the main conclusions are substantiated by providing illustrative examples
Two-point oscillatory solutions to system with relay hysteresis and nonperiodic external disturbance
No full textsummary:We study an -dimensional system of ordinary differential equations with a constant matrix, a relay-type nonlinearity, and an external disturbance in the right-hand side. We consider a nonideal relay characteristic. The external disturbance is described by the product of an exponential function and a sine function with an initial phase as a parameter. We assume the matrix of the linear part and the vector at the relay characteristic such that, by a nonsingular transformation, the system is reduced to the form with the diagonal matrix and the vector being opposite to the unit vector. We establish a necessary and sufficient condition for the existence of two-point oscillatory solutions, i.e., the solutions with two fixed points on the hyperplanes of the relay switching in phase space. Also, we give the sufficient conditions under which such solutions do not exist. We provide a supporting example, which demonstrates how to apply the obtained results